{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Periodic Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import pi\n",
    "from scipy.special import iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x1080 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r_range = np.linspace(-pi, pi, 200)\n",
    "fig, ax = plt.subplots(nrows=3, ncols=1, figsize=(7, 15))\n",
    "\n",
    "ax[0].plot(r_range, np.sin(r_range))\n",
    "ax[1].plot(r_range, np.cos(r_range))\n",
    "ax[2].plot(r_range, np.tan(r_range))\n",
    "ax[2].set_ylim(-20, 20)\n",
    "\n",
    "titles = [r\"$\\sin(\\theta)$\", r\"$\\cos(\\theta)$\", r\"$\\tan(\\theta)$\"]\n",
    "\n",
    "for x, title in zip(ax, titles):\n",
    "    x.grid()\n",
    "    x.set_xticks([-pi, -pi / 2, 0, pi / 2, pi])\n",
    "    x.set_xticklabels([r\"$-\\pi$\", r\"$-\\frac{\\pi}{2}$\", \"0\", r\"$\\frac{\\pi}{2}$\", r\"$\\pi$\"])\n",
    "    x.set_title(title)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(31415926)\n",
    "thetas = np.random.randint(0, 360, size=5)\n",
    "thetas = thetas * pi / 180 # np.deg2rad(thetas)\n",
    "vcos = np.cos(thetas)\n",
    "vsin = np.sin(thetas)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rs = np.linspace(0, 2 * np.pi, 100)\n",
    "\n",
    "plt.figure(figsize=(5, 5))\n",
    "plt.plot(np.cos(rs), np.sin(rs), alpha=0.5)\n",
    "plt.scatter(vcos, vsin, c=\"crimson\")\n",
    "plt.scatter(vcos.mean(), vsin.mean(), c=\"tab:orange\")\n",
    "plt.plot((0, vcos.mean()), (0, vsin.mean()), c=\"tab:orange\")\n",
    "plt.text(vcos.mean(), vsin.mean(), r\"$\\hat \\theta$\", fontsize=20,\n",
    "         horizontalalignment=\"left\",\n",
    "         verticalalignment=\"bottom\");\n",
    "plt.axvline(x=\"0\", c=\"black\", alpha=0.3)\n",
    "plt.axhline(y=\"0\", c=\"black\", alpha=0.3);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The definition of the mean for a set of period variables $\\{\\theta_n\\}_n$\n",
    "$$\n",
    "    \\bar \\theta = \\tan^{-1}\\left(\\frac{\\sum_n \\sin(\\theta_n)}{\\sum_n \\sin(\\theta_n)}\\right)\n",
    "$$\n",
    "\n",
    "Ensures that the location of the mean is **independent** of the origin of the angular coordinate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5698440542329537"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan(vsin.sum() / vcos.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.5698440542329536"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.arctan(np.sin(thetas - pi).sum() / np.cos(thetas - pi).sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## von Misses distributionn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The idea behind the von Mises distribution is to find a gaussian-like distribution along a cirle with unit radius."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vMisses(x0, x1, mu0, mu1, sigma):\n",
    "    return np.exp(- ((x0 - mu0) ** 2 + (x1 - mu1) ** 2) / (2 * sigma)) / (2 * pi * sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, Y = np.mgrid[-3:3:0.005, -3:3:0.005]\n",
    "plt.contour(X, Y, vMisses(X, Y, 0.8, -1, 1), )\n",
    "plt.contour(X, Y, X**2 + Y ** 2 <= 1, cmap=\"Reds\")\n",
    "plt.grid(alpha=0.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The _von Mises_ distribution takes the form:\n",
    "$$\n",
    "    p(\\theta|\\theta_0, m) = \\frac{1}{2\\pi I_0(m)}\\exp(m\\cos(\\theta - \\theta_0))\n",
    "$$\n",
    "\n",
    "Where\n",
    "* $\\theta_0$ is the mean of the distribution\n",
    "* $m$ is the precision of the distribution\n",
    "* $I_0(m)$ is the zeroth-order Bessel function of the first kind"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x8240f1588>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(12, 5))\n",
    "ax1 = fig.add_subplot(121, projection=\"polar\")\n",
    "ax2 = fig.add_subplot(122)\n",
    "\n",
    "params = [(1, 3 * pi / 4), (4, pi / 4), (6, pi * 3 / 2)]\n",
    "\n",
    "for m, theta_0 in params:\n",
    "    npoints = 150\n",
    "    theta = np.linspace(0, 2 * pi, npoints)\n",
    "    von_mises = np.exp(m * np.cos(theta -  theta_0)) / (2 * pi * np.i0(m))\n",
    "\n",
    "    ax1.plot(theta , von_mises);\n",
    "    ax2.plot(theta, von_mises, label=r\"$\\theta_0={:0.2f} \\ m={}$\".format(theta_0, m))\n",
    "ax2.grid(alpha=0.5)\n",
    "ax2.legend(loc=\"lower left\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = np.linspace(0.01, 10)\n",
    "plt.plot(m, iv(0, m))\n",
    "plt.title(\"Zeroth-order Bessel function of the first kind\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute the MLE for $\\theta$ and $m$, we compute the log-likelihood of the von Mises distribution $p(\\theta|\\theta_0, m)$. For $\\hat\\theta_0$, the result is that of the definition for the mean of a periodic variable:\n",
    "\n",
    "$$\n",
    "    \\hat\\theta_0 = \\tan^{-1}\\left(\\frac{\\sum_n \\sin\\theta_n}{\\sum_n \\cos\\theta_n}\\right)\n",
    "$$\n",
    "\n",
    "In order to find $\\hat m$, we arrive at the result\n",
    "\n",
    "$$\n",
    "    A(\\hat m) = \\frac{I_1(\\hat m)}{I_0(\\hat m)} = \\left(\\frac{1}{N}\\sum_n \\cos\\theta_n\\right)\\cos\\hat\\theta_0 + \\left(\\frac{1}{N}\\sum_n \\sin\\theta_n\\right)\\sin\\hat\\theta_0\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 502,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = np.linspace(-1, 10)\n",
    "fig = plt.figure(figsize=(18, 5))\n",
    "ax1 = fig.add_subplot(131)\n",
    "ax2 = fig.add_subplot(132)\n",
    "ax3 = fig.add_subplot(133)\n",
    "\n",
    "I1 = iv(1, m)\n",
    "I0 = iv(0, m)\n",
    "A = I1 / I0\n",
    "\n",
    "ax1.plot(m, iv(0, m), color=\"crimson\")\n",
    "ax1.set_title(\"Zeroth-order Bessel function of the first kind $I_0(m)$\")\n",
    "\n",
    "ax2.plot(m, iv(1, m), color=\"crimson\")\n",
    "ax2.set_title(\"First-order Bessel function of the first kind $I_1(m)$\")\n",
    "\n",
    "ax3.plot(m, A, color=\"crimson\")\n",
    "ax3.set_title(r\"$A(m) = I_1(m) \\ / \\ I_0(m)$\");\n",
    "\n",
    "ax3.set_xlim((0, 10))\n",
    "ax3.set_ylim((0, 1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find $\\hat m$ suffices to invert the function $A$ numerically. This can be done using the bisection method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 619,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7853981633974483"
      ]
     },
     "execution_count": 619,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy.random import vonmises, seed\n",
    "seed(1643)\n",
    "\n",
    "N = 5000\n",
    "sample = vonmises(pi / 4, 6, N)\n",
    "pi / 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 620,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_0 = np.arctan(np.sin(sample).sum() / np.cos(sample).sum())\n",
    "phi = (np.cos(sample).sum() / N) * np.cos(theta_0) + (np.sin(sample).sum() / N) * np.sin(theta_0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 621,
   "metadata": {},
   "outputs": [],
   "source": [
    "def A(m): return iv(1, m) / iv(0, m)\n",
    "def err(Am, phi): return Am - phi\n",
    "\n",
    "def bisection(f, x_plus, x_minus, tol=1e-6, maxiter=500):\n",
    "    niter = 0\n",
    "    while True:\n",
    "        niter += 1\n",
    "        v_plus = f(x_plus)\n",
    "        v_minus = f(x_minus)\n",
    "\n",
    "        x_mid = (x_plus + x_minus) / 2\n",
    "        v_mid = f(x_mid)\n",
    "        if np.sign(v_mid) == np.sign(v_plus):\n",
    "            x_plus = x_mid\n",
    "        else:\n",
    "            x_minus = x_mid\n",
    "\n",
    "        if niter == maxiter:\n",
    "            print(f\"Convergence not successful after {maxiter} tries...\")\n",
    "            return None\n",
    "        elif np.abs(v_mid) < tol:\n",
    "            return x_mid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 622,
   "metadata": {},
   "outputs": [],
   "source": [
    "m_plus, m_minus = 10, -5\n",
    "m_hat = bisection(lambda x: err(A(x), phi), m_plus, m_minus)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 623,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimated theta_0:  0.7984\n",
      "Estimated A(m):     0.9117\n",
      "Estimated hat m:    5.9565\n"
     ]
    }
   ],
   "source": [
    "print(f\"Estimated theta_0: {theta_0:>7.4f}\")\n",
    "print(f\"Estimated A(m): {phi:>10.4f}\")\n",
    "print(f\"Estimated hat m: {m_hat:>9.4f}\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
